In this presentation, we discuss the necessity of using both big data and human judgment for extended probabilistic inference and decision making under uncertainty. The focus is on the analysis of uncertainty in data and judgement and how to model various types of uncertainty in an integrated framework including randomness, ambiguity, inaccuracy and inconsistency. A new Maximum Likelihood Evidential Reasoning (MAKER) framework will be introduced, including its main concepts, key components, evidence space model, state space model, principal evidence combination algorithm, qualitative and quantitative prediction, and decision making processes. The MAKER framework is established to support probabilistic modelling of complex systems, maximum likelihood prediction via data-driven machine learning and evidenced-based decision making under uncertainty. A number of application cases in the areas of healthcare and engineering system maintenance decision making will be presented.